Abe has been pushing for constitutional changes since he returned to the PM's office, and the US has been supportive all along since it means we'll be putting fewer resources into guaranteeing Japan's defense.
This has been in the cards since before TPP even existed.
Abe has been on the path to rearming Japan since 2012[1][2].
The US has wanted Japan to rearm for years. See the articles in the NYT and the WSJ in 2013[3][4]. It's seen as a way to use Japanese money as a counter to China in the region. The fact they are likely to buy US weapons systems helps, too.
The way your comment is phrased makes me wonder if you think the US State department had some legal oversight of the clause or something? It doesn't - the legal basis for this change is completely in Japanese hands.
[1] http://www.cnbc.com/id/100293527
[2] http://www.therecord.com/opinion-story/2623282-is-japan-on-t...
[3] http://www.wsj.com/articles/SB100014241278873240817045782310...
[4] http://www.nytimes.com/2013/01/08/world/asia/with-eye-on-chi...
It doesn't.
Abe went from being very cool on the TPP to coming out in favor (at least in public) almost overnight an the only thing that changed in that period in US-Japan relations was the US state department giving Japan approval to re-militarize. There were virtually no changes to the deal.
Ironically the deal might still fail (which Abe probably wouldn't mind since the TPP is not good for Japan), meaning that this negotiating chip was given away by Obama for free.
>it seems a comparatively minor part in this particular change in Japan's military stance.
You are confusing the reasons why Abe wanted to remilitarize (another topic entirely) with the reasons why Obama had the US state department give him the green light.